CE 3102
Thought Problem 5
Introducing Random Variables
Two types of vehicles use a road, passenger cars and trucks. Observations have indicated
that, over a 2minute interval, the different frequencies of trucks and passenger cars occur
with the following probabilities:
# Passenger Cars=
0
1
2
3
4
0
.03
.09
.09
.06
.03
1
.05
.15
.15
.1
.05
# Trucks=
2
.02
.06
.06
.04
.02
However, a roadtube traffic counter placed on this road is not able to distinguish
between truck and passenger cars, but only counts total vehicles crossing in a 2minute
interval. (a) Characterize the set of outcomes which the tube counter could record, and
determine the associated probability mass function (pmf) and cumulative distribution
function (cdf). (b) What is the expected value and variance of this random variable?
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CE 3102
Fall 2008
Thought Problem 5
Instructor’s Partial Solution
(a) The underlying sample space consists of combinations of truck and passenger car
frequencies, which we can denote as ordered pairs (t,p), where t=truck count, and
p=passenger car count. The function x(.) , denoting the total count, is then formed by
simply adding the truck and passenger car frequencies,
x(t,p) = t+p
If we now let X denote the random variable giving the number of vehicles crossing in a
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 Spring '11
 Probability theory, probability density function, Cumulative distribution function, 2minute interval, passenger car frequencies

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